Decision Making Models for Power Systems Operations Under Uncertainty

Abstract

As the power grids worldwide transition from fossil fuel-based power plants to an era dominated by renewable energy sources (RESs), new operational challenges and uncertainties emerge, particularly for Independent System Operators (ISOs) responsible for grid reliability. The unpredictable nature of RESs introduces challenges in energy production, as evidenced by effects like solar power surges and wind ramping effects. Stochastic modeling can effectively address these challenges, aiming to optimize performance metrics such as expected value, worst-case scenario, and risk. Therefore, the development of new models to handle these uncertainties is necessary. In power system operations, ISOs must ensure the operability and reliability of the system. This is done by planning the energy generation schedule during the day-ahead market in a process known as market clearing. ISOs guarantee a competitive interplay between energy supply and demand in this process, resulting in an energy generator schedule and a competitive market price. This is done by solving the Unit Commitment Problem (UCP), a mathematical optimization problem that guarantees system operability and reliability at a minimal cost. When planning the energy generation schedule, uncertainties such as demand, energy production from RES, and contingencies must be considered. This is usually done using a scenario-based approach, where realizations of uncertainties are generated from fitted probability distributions to be incorporated into the UCP. Thus, the commitment schedule is generated, such as minimizing the expected cost. However, the quality and complexity of solutions depend on the number of scenarios. As uncertainty rises with increased RESs projects, energy generation becomes unpredictable, necessitating more scenarios for accurate cost approximation. This, in turn, increases computational complexity, highlighting the limitations of the scenario generation method. Therefore, it has become critical to devise new approaches to model this problem in the face of such uncertainty. This dissertation provides a new methodology to model the Stochastic Unit Commitment Problem (SUCP) that relies directly on the probability distribution of the random variables, the so-called statistical SUCP. In Chapter 2, a dispatch cost function is derived considering a two-stage approach where the commitment decisions are made in the first stage and remain fixed during the planning horizon. In the second stage, the energy is dispatched based on the commitment decisions of the first stage and the random variables. Then, the expected dispatch cost is derived using the probability distribution of the random residual demand. Thus, an analytical function of the expected dispatch cost is formulated. Since this function is nonlinear, a piecewise linear approximation method is used to linearize the model. The breakpoints of the piecewise linear approximation are determined by stability analysis. A sensitivity analysis is performed to assess the behavior of the expected cost under different levels of hourly correlations of the residual demand. Moreover, a reliability analysis assesses the Loss of Load Probability of the resulting commitment schedule. In Chapter 3, another layer of realism is included in the model by incorporating ramping constraints, ensuring a smooth transition in power output levels from fuel-based generators. Since adding these constraints increases the complexity of the model, different solving strategies are proposed to solve realistic instances of the SUCP. Finally, in Chapter 4, a comparison is made between the proposed statistical SUCP and the scenario-based SUCP to assess the computational complexity, optimality, and stability of the solutions. The comparison is evaluated based on various power system sizes, breakpoints, and scenarios, offering insightful knowledge about the benefits of each model. This dissertation delivers valuable advancements for modeling the SUCP, adding another perspective for ISOs and decision-makers when planning the day-ahead energy generation schedule. The benefits of this research extend to further optimizing power grid operations, reducing costs, and ensuring a reliable transition to renewable energy sources.